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Webster 1913 Edition

Hyperboloid

Hy-per′bo-loid

,
Noun.
[
Hyperbola
+
-oid
: cf. F.
hyperboloïde
.]
(Geom.)
A surface of the second order, which is cut by certain planes in hyperbolas; also, the solid, bounded in part by such a surface.
Hyperboloid of revolution
,
an hyperboloid described by an hyperbola revolving about one of its axes. The surface has two separate sheets when the axis of revolution is the transverse axis, but only one when the axis of revolution is the conjugate axis of the hyperbola.

Hy-per′bo-loid

,
Adj.
(Geom.)
Having some property that belongs to an hyperboloid or hyperbola.

Webster 1828 Edition

Hyperboloid

HYPER'BOLOID

,
Noun.
[hyperbola, and Gr. form.] A hyperbolic conoid; a solid formed by the revolution of a hyperbola about its axis.

Definition 2024

hyperboloid

hyperboloid

English

Noun

an hyperboloid of one sheet

hyperboloid ‎(plural hyperboloids)

  1. A particular surface in three-dimensional Euclidean space, the graph of a quadratic with all three variables squared and their coefficients not all of the same sign.

Usage notes

  • If the hyperboloid is a connected surface, it is said to be of one sheet; otherwise, it has two components and is said to be of two sheets.
  • Like many terms that start with a non-silent h but have emphasis on their second syllable, some people precede hyperboloid with an, others with a.

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